Question

A bulletin board has a perimeter of 200 inches. Which equation expresses the area A(w) of the bulletin board as a function of its width, w?

A. A(w) = 100w - w2
B. A(w) = 200w - w2
C. A(w) = w2 – 100w
D. A(w)=w2 - 200w​

Answer 1

The equation that expresses the area A(w) of the bulletin board as a function of its width w is A(w) = w².

Step-by-step explanation:

To express the area A(w) of the bulletin board as a function of its width, we need to find the equation that relates the width to the area. Since the perimeter of the bulletin board is given as 200 inches, we can use the formula for the perimeter of a rectangle: P = 2w + 2l, where w is the width and l is the length. Since the bulletin board is assumed to be a rectangle, the length is equal to the width. We can rewrite the formula as 2w + 2w = 200, which simplifies to 4w = 200. Solving for w, we find w = 50.

Now that we know the width, we can express the area A(w) as a function of w. Since the area of a rectangle is given by the formula A = length * width, and the length is equal to the width in this case, we have A(w) = w * w = w².

The correct equation that expresses the area A(w) of the bulletin board as a function of its width w is A(w) = w², which corresponds to option D.

Answer 2

Answer: A(W) = 100W -
`W^(2)`

Step-by-step explanation:

The formula for calculating the perimeter is given as :

P = 2 ( L + W )

the perimeter is given as 200 , that is

200 = 2 ( L + W )

Dividing through by 2 , we have

100 = L + W

Make L the subject of the formula ;

L = 100 - W

The formula for the area is given as Length x width , substituting the values , we have :

A = LW , since , L = 100 - W , we have

A = (100- W) (W)

A = 100W -
`W^(2)`

Therefore :

A(W) = 100W -
`W^(2)`